Question: Simplify to lowest terms. $\dfrac{72}{54}$
There are several ways to tackle this problem. What is the greatest common factor (GCD) of 72 and 54? $72 = 2\cdot2\cdot2\cdot3\cdot3$ $54 = 2\cdot3\cdot3\cdot3$ $\mbox{GCD}(72, 54) = 2\cdot3\cdot3 = 18$ $\dfrac{72}{54} = \dfrac{4 \cdot 18}{ 3\cdot 18}$ $\hphantom{\dfrac{72}{54}} = \dfrac{4}{3} \cdot \dfrac{18}{18}$ $\hphantom{\dfrac{72}{54}} = \dfrac{4}{3} \cdot 1$ $\hphantom{\dfrac{72}{54}} = \dfrac{4}{3}$ You can also solve this problem by repeatedly breaking the numerator and denominator into common factors. For example: $\dfrac{72}{54}= \dfrac{2\cdot36}{2\cdot27}= \dfrac{2\cdot 3\cdot12}{2\cdot 3\cdot9}= \dfrac{2\cdot 3\cdot 3\cdot4}{2\cdot 3\cdot 3\cdot3}= \dfrac{4}{3}$